I do not know how complementarity is applied to this scenario - anyone else have a suggestion?
On Sat, Aug 14, 2004 at 04:56:12PM -0700, Fred Chen wrote: > Russell, I agree with what you state below. But consider the following > experiment. > > Instead of two beams of equal intensity interfering, as in classical > inteferometry, one has unequal amplitude beams. Specifically, > > Beam A: 0.9*exp(iax+ibz-iwt) > Beam B: 0.1*exp(-iax+ibz-iwt) > > The interference pattern is of the form: > > Interference field = [cos(ax)+i*0.8sin(ax)]exp(ibx-iwt) > > So the resulting photon distribution follows the intensity, or the field > amplitude squared: > > Interference intensity = 0.64+ 0.36*cos^2(ax) > > This wave pattern will begin to appear after sufficient number of > photons, but each photon is always ~99% (81/82) likely to have > originated from Beam A, based on conservation. > > If Beam A and Beam B had different amplitudes, you would maximize the > uncertainty of the photon origin since you have to say 50/50 likelihood > for a photon coming from either A or B. > > The complementarity principle's strongest statement is 100% certainty, > and that cannot be attained. But we can still get an idea of the wave > interference pattern and 'which way' information with high (but not > 100%) certainty in gray-transition cases such as above. > > Fred > > -----Original Message----- > From: Russell Standish [mailto:[EMAIL PROTECTED] > Sent: Saturday, August 14, 2004 2:51 AM > To: Fred Chen > Cc: 'Everything List' > Subject: Re: Quantum Rebel > > > On Fri, Aug 13, 2004 at 11:43:10PM -0700, Fred Chen wrote: > ... > > > > > A better (and far simpler) way to challenge complementarity would be > > to use a low-intensity interferogram in a photographic film or CCD. At > > > first the photons being detected are few so the shot (particle-like) > > aspect is more obvious. As more photons are integrated, the classical > > interference pattern is observed. Can there be a transition region > > where both aspects are observable? > > > > This does not challenge complementarity. Consider a double slit > apparatus with the photon source's intensity down so low that each > individual photon can be observed hitting the screen one at a time. But > when one plots the distribution of positions where the photons strike > the screen after observing many of them, the interference pattern > results. This is simple and uncomplicated, but is not what the > complementarity principle is about. > > Now consider that you have information about which slit the photon > passed through before hitting the screen - ie each photon is labelled 1, > 2, 1, 1, etc, according to whuch slit it passed through. Therefore, you > can separate the observed photons into two sets, according to which slit > the phtons passed through. The distribution of each subset corresponds > to a single slit experiment, and the final distribution must be the sum > of the two single slit experiements. But single slit experiments do not > have interference patterns - hence the sum cannot have an interference > pattern either. > > Consequently, if you have any way of knowing which slit the photon went > through (the "which way" information), then you cannot have an > interference pattern. This is what the complementarity principle means. > > Cheers > -- > *PS: A number of people ask me about the attachment to my email, which > is of type "application/pgp-signature". Don't worry, it is not a virus. > It is an electronic signature, that may be used to verify this email > came from me if you have PGP or GPG installed. Otherwise, you may safely > ignore this attachment. > > ------------------------------------------------------------------------ > ---- > A/Prof Russell Standish Director > High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 > (mobile) > UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 > (") > Australia [EMAIL PROTECTED] > > Room 2075, Red Centre > http://parallel.hpc.unsw.edu.au/rks > International prefix +612, Interstate prefix 02 > ------------------------------------------------------------------------ > ---- > -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 (") Australia [EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------
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